Approximating the Total Variation with Finite Differences or Finite Elements

Antonin Chambolle*, Thomas Pock

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


We present and compare various types of discretizations which have been proposed to approximate the total variation (mostly, of a gray-level image in two dimensions). We discuss the properties of finite differences and finite elements based approach and compare their merits, in particular in terms of error estimates and quality of the reconstruction.

Original languageEnglish
Title of host publicationHandbook of Numerical Analysis
EditorsAndrea Bonito, Ricardo H. Nochetto
Number of pages35
Publication statusPublished - Jan 2021

Publication series

NameHandbook of Numerical Analysis
ISSN (Print)1570-8659


  • error bounds
  • finite differences
  • finite elements
  • Image processing
  • numerical analysis
  • total variation

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics
  • Numerical Analysis
  • Modelling and Simulation


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